This application claims priority of the German Patent Application No. 102 04 943.2, filed Feb. 7, 2002, which is incorporated by reference herein.
The invention concerns a method for the determination of layer thicknesses and optical parameters of a number of layers of a specimen, in which the reflectance spectrum of the specimen is measured and subsequently smoothed, and a modeled reflectance spectrum is adapted to the measured one so as thereby to determine the layer thicknesses; and refers to the problem of determining the thicknesses of multiple-layer systems.
Reflection spectrometry is a method, widely used and known for some time, for the examination of layered systems, in particular wafers, and for the determination of layer thicknesses and other optical parameters. The principle of the method is very simple: a specimen that has multiple layers is irradiated with light of a defined wavelength. If the layers are transparent, the light penetrates into the media and is partially reflected in the transition regions between two layers, including the transition between the topmost layer and the ambient atmosphere. The superimposition of incident and reflected light results in interferences, thus influencing the intensity of the reflected light. The ratio between the intensities of the incident and the reflected light determines the so-called absolute reflectance; both intensities must therefore be measured. If the wavelength is then varied continuously within a defined range, this yields a reflectance spectrum that, as a function of the wavelength, has maxima and minima that are produced by the interferences. The locations of these extremes depend on the material properties of the specimen, which determine the optical behavior. These optical parameters include, for example, the refractive index and absorption coefficient. The layer thickness additionally influences the location of the extremes in the reflectance spectrum.
It is possible, in principle, to deduce these parameters from the measured reflectance spectrum; in an ideal model, the limits in terms of the thickness and number of layers are very wide. The basic formulae can be derived from Fresnel refraction theory, as described in detail in the article xe2x80x9cPolycrystalline silicon film thickness measurement from analysis of visible reflectance spectraxe2x80x9d by P. S. Hauge in J. Opt. Soc. Am., Vol. 69 (8), 1979, pp. 1143-1152. As is evident from the book by O. Stenzel, xe2x80x9cDas Dxc3xcnnschichtspektrumxe2x80x9d [The thin-layer spectrum], Akademieverlag 1996, pp. 77-80, the determination of optical constants and layer thicknesses by back-calculation in reality turns out to be very difficult and laborious, however, since the number of unknowns is very large.
One must therefore resort to approximations, or apply limitations. Thickness determination is simplest if the number of layers is limited to one layer whose thickness is to be determined. In this case a correlation can be created between the layer thickness d and the refractive indices n(xcexi) for the wavelengths xcexi that belong to the extremes in the reflectance spectrum, where the index i indicates the extremes. If the reflectance spectrum contains a total number m of extremes between two arbitrarily selected extremes xcexi and xcexj, the layer thickness can then be determined using the equation                     d        =                              1            4                    ·                                    m              -              1                                                                        n                  ⁡                                      (                                          λ                      i                                        )                                                                    λ                  i                                            -                                                n                  ⁡                                      (                                          λ                      j                                        )                                                                    λ                  j                                                                                        (        1        )            
To arrive at this expression, however, the limiting assumption of only one weakly dispersive layer must be applied; this formula fails with strong dispersion and with absorbent layers. This limits the class of materials that can be investigated. A further prerequisite is that the wavelength-dependent refractive index n(xcex) be known. This principle, hereinafter called the xe2x80x9cextremes method,xe2x80x9d is the basis of, for example, the method described in U.S. Pat. No. 4,984,894 for determining the layer thickness of a layer.
U.S. Pat. No. 5,440,141 describes a method for determining the thicknesses of three layers. In this, an approximate thickness of the first layer is determined using the aforementioned xe2x80x9cextremes method.xe2x80x9d The exact thickness of the first layer is then determined by calculating, in a region approximately xc2x1100 nm around this value and for various thicknesses, firstly a modeled reflectance spectrum and secondly the deviations of the respective modeled reflectance spectrum from the measured spectrum. These deviations are combined into an error function E min which the deviations are squared:                     E        ∼                              ∑                          λ              i                                ⁢                      xe2x80x83                    ⁢                                                                      w                                      λ                    i                                                  ⁡                                  (                                                                                    R                        ex                                            ⁡                                              (                                                  λ                          i                                                )                                                              -                                                                  R                        th                                            ⁡                                              (                                                  λ                          i                                                )                                                                              )                                            2                        .                                              (        2        )            
where wxcex is a weighting factor, Rex the experimentally determined reflectance spectrum, and Rth the modeled reflectance spectrum for a layer thickness. This layer-thickness-dependent function E is then minimized by looking for the modeled reflectance spectrum at which the deviations are smallest. The layer thickness at which the function E is minimal is identified as the actual layer thickness. With multiple layers, however, this method can be implemented only if the first layer reflects in a first wavelength region in which the lower layers absorb light, so that they can be left out of consideration when determining the thickness of the first layer. In the document cited, reflection measurements are therefore performed in two different wavelength regions.
To determine an approximate thickness of the second layer, a frequency analysis of the reflectance spectrum in the second wavelength region is performed, based on the fact that maxima and minima repeat periodically in the reflectance spectrum; this is expressed in the converted spectrum by the presence of more or less pronounced peaks. These peaks allow an initial approximate conclusion as to the thickness of the second layer. An approximate thickness of the third layer is obtained by lowpass filtration, the differing material properties of the layer stack once again being exploited here. Similarly to the procedure for the first layer, an error function dependent on the thicknesses of the second and third layers is minimized, by looking for those thicknesses at which the deviations between the experimental and modeled spectra are smallest.
It is thus clearly evident from U.S. Pat. No. 5,440,141 that the thicknesses of multiple layers can be determined, but that this works only for layer combinations of specific materials.
Lastly, U.S. Pat. No. 5,493,401 describes a method for determination of the thicknesses ofxe2x80x94in principlexe2x80x94an arbitrarily large number of layers. This is done by first determining the total number of extremes as well as the smallest and largest wavelength that corresponds to one extreme. From these magnitudes, conclusions can be drawn as to the total thickness of the layer stack, i.e. the summed thicknesses of the individual layers. For each of the various combinations of individual thicknesses that together yield the total thickness, a modeled reflectance spectrum is then calculated and an error function E, containing the deviations between the modeled and the experimental reflectance spectrum, is determined as described above. That combination of thicknesses for which those deviations are smallest is then found.
The applicability of the method described in U.S. Pat. No. 5,493,401 is also limited, however. As soon as the experimental spectrum is more greatly modified by influences that the model does not, or does not adequately, account for, the results are no longer reliable, and what is obtained is very probably an incorrect set of layer thicknesses for which the function E assumes a local minimum. Light scattering, such as occurs e.g. in polysilicon, and specimen surface roughness influence e.g. the expression of the extremes: at high levels of roughness and diffusion, certain extremes will be less pronounced, i.e. will have lower reflectance, than actually predicted in the model. Insufficient spectral resolution of the spectrometer can also cause changes. The materials also must be known, since both the refractive indices and the absorption constants must be defined. Severe dispersion or absorption also acts to modify the expression of the extremes. Deviations can therefore occur between the modeled and experimental reflectance spectra, especially in the UV region where absorption is high; the method described in U.S. Pat. No. 5,493,401 is therefore also preferably used at wavelengths in the range from 400 to 800 nm. These factors that can modify the experimental reflectance spectrum are not taken into account, or are considered only insufficiently, in all the theoretical models on which the various evaluation models are based. The greater the deviations between the modeled and measured reflectance spectra, the greater the uncertainty in the search for a minimum for the error function, i.e. in the determination of the optimum layer thicknesses; and in some circumstances that search is entirely unsuccessful. One of the results has been that depending on the specimen system, a particular adapted model is used that yields acceptable results for specific material combinations but fails with other specimen systems.
Proceeding from this existing art, it is the object of the invention to develop a method with which the optical parameters and thicknesses of multiple-layer systems can be determined more reliably than heretofore, and which reacts less sensitively to interfering factors that influence the reflectance spectrum.
According to the present invention, in a method of the kind described above encompassing, in a first step, introducing a specimen, having a number N of layers whose thicknesses are to be determined, into a measurement arrangement and measuring the reflectance spectrum of the specimen in a defined wavelength region; in a second step, smoothing the measured reflectance spectrum by a reduction equivalent to noise caused predominantly by external influences; in a third step, selecting a set S1 of a number M of wavelengths xcex1,i, where i=1, . . . , M, arranged in order of size, each wavelength xcex1,i in the set S1 corresponding to a respective local extreme in the smoothed reflectance spectrum and the selection being performed under the condition that two adjacent extremes differ by at least one defined contrast criterion, and that one of the two extremes is a minimum and the other a maximum; in a fourth step, adapting a modeled reflectance spectrum in stepwise fashion to the smoothed reflectance spectrum for the number N of layers, using a model, in which layer thicknesses, or layer thicknesses and optical parameters, are defined as variable magnitudes, in each adaptation step a set S2 of a number M of wavelengths xcex2,j, where j=1, . . . , M, arranged in order in the same fashion as in the set S1, being selected, each wavelength xcex2,j in the set S2 corresponding respectively to a local extreme in the modeled reflectance spectrum, and the selection being performed under the condition that of two adjacent extremes, the one is a minimum and the other a maximum, and in each adaptation step an optimization criterion furthermore being determined, the best adaptation corresponding to a minimum of the optimization criterion so that the actual layer thickness can substantially be determined, the object is achieved in that the optimization criterion is determined by the totality of the absolute values of the wavelength differences of all pairs of wavelengths (xcex1,i, xcex2,i), where i=1, . . . , M.
The new method is based on the astonishing realization that adapting the positions of the extremes in the model to the positions of the extremes in the experimental spectrum is sufficient to allow an accurate layer thickness determination to be made. The totality of the differences in the pairs of wavelengths is the decisive criterion here. To prevent positive and negative differences from possibly canceling one another out and yielding an incorrect set of layer thicknesses, the absolute values are considered.
It is preferable to consider the sum of the squares of the differences, since if optimization is to take place with the aid of a calculation system, fewer calculation operations are necessary in this case than if the absolute value is considered. Other functions in which the differences between respective pairs of wavelengths participate as absolute values are also conceivable, however, e.g. polynomial functions.
With a large number of extremes and a large number of specimens to be examined, it is additionally advantageous to weight the sum with the number M of extremes; this can then be employed simultaneously to assess the quality of the adaptation for various specimens.
Because only the wavelengths and not (as with the methods used previously) the reflectance spectra are compared in the method according to the present invention, the new method is less dependent on interfering influences, The result is therefore not influenced by whether and how reflectances are damped, provided they can be measured and are present in the smoothed reflectance spectrum. Even wavelengths at which the absorptivity of the specimen is so high that the extremes are greatly dampedxe2x80x94but still recordablexe2x80x94can be used for investigation. Materials for which investigation with existing methods was difficult or impossible are also easily accessible to the method according to the present invention, for example polysilicon, which exhibits a high level of light scattering because of the many different crystal directions. Thick layers can also easily be analyzed. Layers up to 50 xcexcm in thickness can be investigated with the new method. In principle, even systems with many layers are accessible to the method, although adaptation with more than seven layers is very time-consuming if current standard home computers are used for evaluation and adaptation.
A further advantage of the method is the fact that optical parameters can also be determined, i.e. that layered systems made of unknown materials can also be investigated.